Statistics and Probability Commons^™

On The Gumbel-Weibull{Cauchy} Distribution, Jennifer D. Pippin

Theses, Dissertations and Capstones

Developing new statistical distributions and seeking higher flexibility in modeling different shapes of data remain a strong emphasis in research. The T-R{Y } framework, introduced in [3], utilizes three statistical distributions in order to generate a new distribution. Many research papers appeared in literature to develop distributions based on the T-R{Y } framework. In this thesis, a member of the T-R{Y } framework, namely the Gumbel-Weibull{Cauchy} (GWC), is introduced. Statistical properties of the GWC are studied, such as the quantile function, the hazard function, transformations, Shannon entropy, the …

Floquet Theory For First-Order Delay Equations And An Application To Height Stabilization Of A Drone’S Flight, Martin Bohner, Alexander Domoshnitsky, Oleg Kupervasser, Alex Sitkin

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we proposed a version of the Floquet theory for delay differential equations. We demonstrated that very natural assumptions for control in technical applications can lead us to a one-dimensional fundamental system. This approach allowed researchers to work with classical methods used in the case of ordinary differential equations. On this basis, new original unexpected results on the exponential stability were proposed. For example, in the equation x' (4)+a(t)x(t—-T(7)) = 0, t € [0, co), we avoided the assumption on the smallness of the product sup,j9,.) 41 SUP;< {9,00) TD) < 3/2 for asymptotic stability. We obtained that in the case of w-periodic coefficient and delay, the fact that the period w was situated in a corresponding interval can lead to exponential stability. We then applied our new tests of stability to the stabilization of a drone's flight, where smallness of the noted above product could not be achieved from a technical point of view. For an equation with periodic coefficient and delay, we got a formula of the solution's representation on the semiaxis.

Gompertz Distribution On Time Scales, Wasiu Sule

Theses, Dissertations and Capstones

We shall investigate Gompertz dynamic equations within the context of time scales calculus, by exploring the mathematical foundations and applications of the Gompertz model, which is commonly used to describe growth phenomena in various fields such as biology and economics. This research seeks to analyze the Gompertz cumulative distribution functions (CDF) and probability density functions (PDF) across different time scales, including the real numbers R and integer multiples hN. Probability techniques will be used to derive the CDF and PDF associated with the Gompertz dynamic equations, and we will examine how varying the time scale impacts the characteristics …

A Unified Concept Of Periodicity On Any Time Scale And Applications, Martin Bohner, Jaqueline G. Mesquita, Sabrina H. Streipert

Mathematics and Statistics Faculty Research & Creative Works

We introduce a novel definition of periodicity on arbitrary time scales, dependent on a strictly increasing and differentiable function. This removes the commonly used and restrictive assumption of a periodic time scale to define periodic functions. Our new definition furthermore allows for a wider class of functions to be studied using the theory of periodic systems. After providing crucial properties of these periodic functions, such as the translation invariance of integrals of periodic functions, we apply the concept of this new periodicity to linear dynamic equations. We provide necessary and sufficient conditions for a linear dynamic equation to have such …

The Discrete Generalized Proportional Fractional Derivative, Martin Bohner, Rajrani Gupta

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we have introduced a discrete generalized proportional fractional derivative and generated Riemann-Liouville and Caputo discrete generalized proportional fractional derivatives. The Laplace transforms of the discrete generalized proportional fractional derivatives and integrals are also calculated.

Empirical Vulnerability Function Development Based On The Damage Caused By The 2014 Chiang Rai Earthquake, Thailand, Patcharavadee Hong, Masashi Matsuoka

Institute for Innovation & Entrepreneurship Publications

Seismic hazards in Thailand are frequently overlooked in disaster management planning, leading to insufficient research and significant economic losses during earthquake events. The 2014 Chiang Rai earthquake exposed critical vulnerabilities in Thailand's building practices due to widespread non-compliance with building codes and limited preparedness. This exposure prompted the development of empirical vulnerability functions using loss data from 15,031 damaged residences. The study analyzed government compensation records, which were standardized using replacement cost metrics. Three distinct models were developed through probabilistic and possibilistic modeling approaches. Residual analysis demonstrated the superior performance of the possibilistic approach, with the Possibilistic-based Vulnerability Function achieving …

Predicting Superconducting Critical Temperature From Composition-Derived Features: A Transparent Linear And Regularized Regression Study, Md Ahiduzzaman

Data Science and Data Mining

We study prediction of superconducting critical temperature (Tc) from 81 composition-derived descriptors across 21,263 materials. To keep the analysis transparent and repro- ducible, we focus on linear models: Ordinary Least Squares (OLS), Ridge, Lasso, and Elastic Net (ENet). All models share a single evaluation protocol (5-fold cross-validation with standardized inputs) and are compared on RMSE, MAE, and R2. On this feature set, OLS attains the best cross-validated performance (RMSE = 17.6 K, MAE = 13.3 K , R2 = 0.735), with Lasso/ENet essentially tied next (RMSE ≈ 17.7 K , R2 ≈ 0.734); Ridge underperforms (RMSE = 18.9 K , …

Comparative Analysis Of Lasso, Ridge, And Elastic Net For Variable Selection In High-Dimensional Maize Data, Md Ahiduzzaman

Data Science and Data Mining

In high-dimensional genomic data analysis, traditional linear regression techniques often struggle due to the presence of a large number of predictor variables relative to observations. Penalized regression methods such as LASSO, Ridge, and Elastic Net have emerged as effective solutions by imposing regularization, which helps in managing multicollinearity and enhancing prediction accuracy. This study applies these techniques to the Maize dataset to model the time to male flowering, selecting relevant genetic markers as predictors. Our findings suggest that Elastic Net is particularly effective for high-dimensional data with correlated variables, achieving a balance between prediction accuracy and variable selection. The results …

Enhanced Kneser-Type Oscillation Criteria For Second-Order Functional Quasilinear Dynamic Equations On Time Scales, Taher S. Hassan, Elvan Akın, Bassant M. El-Matary, Ioan Lucian Popa, Mouataz Billah Mesmouli, Ismoil Odinaev, Akbar Ali

Mathematics and Statistics Faculty Research & Creative Works

This work presents new Kneser-type oscillation criteria for second-order quasilinear functional dynamic equations defined on arbitrary unbounded above time scales. Our approach employs the Riccati transformation technique in conjunction with the integral averaging method. The results show a significant improvement over recent Kneser-type oscillation criteria. We provided several illustrative examples to highlight the importance of our findings.

An Evaluation On The Uncertainty For The Routine Of Dosimetry Calibration At The National Secondary Standard Dosimetry Laboratory, Albania, Klotilda Nikaj

International Journal of Nuclear Security

Every employer must, in relation to any work with ionizing radiation that they undertake, take all necessary steps to restrict so far as is reasonably practicable the extent to which their employees and other persons are exposed to ionizing radiation. This goal leads to an increased awareness about the proper maintenance and annual calibration of the personal dosimeters to ensure an accurate and precise radiation dose. The present work has described the performance of the radiation system of the ¹³⁷Cs source at the National Secondary Standard Dosimetry Laboratory (SSDL), located at the Institute of Applied Nuclear Physics at the …

Gaps In Knowledge: Topological Insights Into The Structure Of Science, Gavin Engelstad

Mathematics, Statistics, and Computer Science Honors Projects

Understanding scientific development is essential to ascertaining the mechanisms leading us into the future. Building this understanding requires both methodological developments and empirical research. This thesis contributes in both aspects using a topological approach to examine scientific knowledge. The first section presents a new algorithm to find optimal cycle representatives for homological features in complex networks, a context for which we demonstrate existing algorithms can be inadequate. The second section applies a number of topological methods, including our cycle optimization algorithm, to data on individual scientific fields, demonstrating the value of topological approaches and highlighting new insights about how science …

Handwritten Digit Recognition Using Machine Learning Classifiers, Md Ahiduzzaman

Data Science and Data Mining

This project explores and compares the performance of various machine learning classifiers for handwritten digit recognition using the MNIST dataset. The classifiers include Logistic Regression, k-Nearest Neighbors, and Convolutional Neural Networks. Each classifier is evaluated based on accuracy, precision, recall, F1-score, and confusion matrix analysis.

Statistical Analysis Of Climate Trends And Variability In Tarrant County Using Annual, Decade, And Three-Decade Time Periods, Quinnton Debolt

Earth & Environmental Sciences Theses - Archive

This study is a statistical analysis of climate trends within the Dallas-Fort Worth metroplex according to several time-scale models to understand how the climate for the locality has changed and to provide a basis for projections of what future climate might look like. Trends in mean temperature and precipitation for North Central Texas generally correlate with corresponding global trends linked to natural variability and anthropogenic-induced climate change. Temperature rises in this region annually by 0.08°C and by 0.22°C for a three-decade average. Seasonal increases in three-decadal averages of temperature for North Central Texas relative to the average of the reference …

A New Formulation Of Hardy-Type Dynamic Inequalities On Time Scales, Martin Bohner, Irena Jadlovská, Ahmed I. Saied

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we introduce a novel formulation of dynamic Hardy-type inequalities on a time scale, motivated by a recently established convexity approach in the Haar measure. The classical Hardy inequality is refined so that the classical Lebesgue-measure constant is replaced by the sharp constant 1. We obtain time-scale analogues on finite intervals with best constants, and, for nonincreasing and nondecreasing functions, reversed inequalities with explicit weights described by incomplete β-functions. To establish our results, we employ two distinct time scales and apply the chain rule, together with the substitution rule, the derivative of inverse functions, and Fubini's theorem for …

Analysis Of Errors In The Management Of Cutaneous Disorders, Robert J. Pariser, Sarah Alnaif

Department Dermatology Faculty Publications

In this study, we prospectively and retrospectively evaluated the occurrence of errors in the management of cutaneous disorders from patient visits and medical records in a single dermatology practice in southeast Virginia over a 3-year period (June 2020-July 2023). Providers should be able to improve diagnostic accuracy by utilizing established rapid bedside diagnostic techniques.

The Economic And Environmental Impact Of Shinkansen And High-Speed Rail Infrastructure: A Comparative Analysis Of Economic Growth And Carbon Emissions Reduction, Dillan R. Victory

SPARK Symposium Presentations

The development of Japan's high-speed rail system, the Shinkansen, has played a pivotal role in the country's post-war economic resurgence. Introduced in 1964 with the Tokaidō Shinkansen, this transformative infrastructure investment significantly reduced travel times, bolstered economic activity around station hubs, and facilitated regional development by enabling urban decentralization. This paper explores the long-term economic benefits of high-speed rail, including its impact on land value, business expansion, and carbon emissions. The case study of the Linear Chuo Shinkansen, Japan's latest maglev project, underscores both the economic promise and the political resistance to expansion, particularly in regions such as Shizuoka.

Using …

Generalizations Of Finiteness Conditions And Extension Monads In Algebras With Infinitely Many Or Infinitary Operations, Danielle Christienne Bowerman

Doctoral Dissertations

In this work, we extend the results of finiteness conditions and extension monads found in Insall from finitely many finitary operations to infinitely many finitary operations, as well as touching on infinitary operations. We also examine varieties of algebras, including the notion of strong varieties introduced in Insall, and common constructions of extension monads in varieties of algebras. We see that for finite collections of algebras of the same signature, the extension monad operation on a variety of algebras commutes with the direct product operation, and all retractions from an enlargement or extension monad are trivial. We also see that …

Beyond Homogeneity: Exploring Causal Heterogeneity In Psychopathology, Philip B. Vinh

Theses and Dissertations

Traditional models in psychiatric research often impose assumptions of causal homogeneity, treating population-level associations as reflective of uniform underlying mechanisms. This dissertation challenges that assumption by introducing statistical and machine learning frameworks designed to detect and model causal heterogeneity in the development of psychopathology. Central to this approach is the advancement of finite mixture structural equation modeling (FM-SEM) to identify latent subgroups characterized by distinct, and sometimes opposing, causal pathways.

The dissertation comprises three integrated empirical studies. The first introduces mixDoC, a finite mixture extension of the classical Direction of Causation (DoC) model applied to twin data, enabling the detection …

Predictive Inference For Ion Concentration With Machine Learning And Bayesian Methods, Alexandra B. Ulbing

Theses and Dissertations

Ultraviolet--visible (UV--Vis) spectroscopy produces high-dimensional signals that are strongly collinear, shift with concentration, and exhibit heteroskedastic, non-Gaussian noise. These features make supervised regression from spectra to ionic concentrations statistically challenging and limit the reliability of methods that assume linear structure or homoscedastic errors.

This dissertation develops two complementary frameworks for prediction and uncertainty quantification in UV--Vis spectroscopic regression: (1) frequentist stacked ensembles combined with distribution-free conformal prediction, and (2) Bayesian hierarchical modeling and Bayesian stacking. Together, they provide a unified view of model-based and distribution-free uncertainty across nickel and nickel--cobalt datasets.

The frequentist component builds ensembles of Functional Data Analysis …

Predicting Capture And Survival Probabilities Of The Arizona Tiger Salamander: A Comparison Of Capture-Recapture Models, Brittney Nelson

Murray State Theses and Dissertations

Capture-recapture models are essential tools for estimating population dynamics in ecological studies. A fundamental component of these models is the capture history matrix, which records individual detection over time and serves as the basis for estimating survival and capture probabilities. This presentation explores three statistical approaches to these estimations: the Cormack-Jolly-Seber (CJS) model, the Hidden Markov Model (HMM) for CJS, and the Bayesian CJS model. The CJS model provides a likelihood-based framework for estimation, and the HMM CJS incorporates latent states into the model to account for uncertainty in detection. The Bayesian CJS extends this same analysis by integrating prior …

Ms-Yolo: Infrared Object Detection For Edge Deployment Via Mobilenetv4 And Slideloss, Jiali Zhang, Thomas S. White, Haoliang Zhang, Wenqing Hu, Donald C. Wunsch, Jian Liu

Mathematics and Statistics Faculty Research & Creative Works

Infrared imaging has emerged as a robust solution for urban object detection under low-light and adverse weather conditions, offering significant advantages over traditional visible-light cameras. However, challenges such as class imbalance, thermal noise, and computational constraints can significantly hinder model performance in practical settings. To address these issues, we evaluate multiple YOLO variants on the FLIR ADAS V2 dataset, ultimately selecting YOLOv8 as our baseline due to its balanced accuracy and efficiency. Building on this foundation, we present MS-YOLO (MobileNetv4 and SlideLoss based on YOLO), which replaces YOLOv8's CSPDarknet backbone with the more efficient MobileNetV4, reducing computational overhead by 1.5% …

Optimizing Decision-Making In A Cerebral Palsy Model Using Reinforcement Learning, Richard Ampah

Pitzer Senior Theses

This study presents an original interdisciplinary investigation into how reinforcement learning (RL) can model motor and cognitive defects and potentially improve motor and cognitive functions in individuals with cerebral palsy (CP), a non-progressive neurological disorder that impairs movement and adaptability. Integrating computational neuroscience and machine learning, the research applies policy gradient methods and Markov Decision Processes (MDPs) to simulate adaptive learning in agents with and without CP-related constraints.

The central aim is to compare the cumulative rewards of optimal policies, derived from value iteration, and human-like learning policies using the REINFORCE algorithm, both with and without the Bellman baseline. The …

Local Limit Theorems On Finitely Generated Abelian Groups, Yutong Yan

Honors Theses

In this thesis, we classify the pointwise behavior of finite-range random walks on finitely generated abelian groups in terms of local limit theorems. Random walks are central objects of research in probability theory, and the theory has found applications in statistics, physics, and even card shuffling. One significant topic in this line of study is random walks on finitely generated groups. Starting from the pioneering work of G. Pólya and H. Kesten, random walks on finitely generated groups have been studied extensively. However, many notable results on the subject (local limit theorems, for example) make assumptions about periodicity and irreducibility …

Fault Tree Analysis For Robust Design, Jonathan Degroff, Gene Jean-Win Hou

Mechanical & Aerospace Engineering Faculty Publications

The objective of this research is to incorporate system failure into a robust design formation and solution process. The system failure referred to here will be built using fault tree analysis (FTA), which will take all lower-level failure events into consideration. Two examples are investigated here. One will directly treat the probabilities of the basis events as design variables, The other will be formulated in five different models: deterministic design optimization, the reliability index-based, the “and” gate-based, the “or” gate-based and the “inhibit” gate-based robust design. Their corresponding optimization solutions will be compared with each other. The post-optimality analysis of …

Comparative Study Of Single Imputation Techniques For The Prediction Of Missing Dairy Data, Ahmed M. Gad Prof, Ahmed Abdelhakim Ahmed Mr, Eman Manaa Prof, Basant Shafik Dr, Sakr Mostafa Prof

Business Administration

Dairy farm records are a crucial component of effective livestock business management. Record analysis allows a farm’s owner to make informed decisions. Incomplete records are less useful for data analysis, so it's important to handle missing values correctly. This study compares different imputation methods for handling missing values in a dataset of dairy records comprising 997 records collected from 234 cows between 2012 and 2022. The dataset was screened against records with missing values and then deleted, resulting in 858 observations from 200 animals. There were missing values in two variables, with a missing percentage of 13.9%: days in milk …

A New Robust Imputation Method For Longitudinal Data With Non-Normal Continuous Outcomes, Ahmed M. Gad Prof, Yasmie A. Mohamed, Nesma M. Daewish Dr, Abdelnaser S. Abdrabou Prof, Wafaa M. Ibrahim Dr

Business Administration

Missing values is very common in longitudinal data and it is the main challenge in analysis of longitudinal data. Missing values have a significant effect on longitudinal data analysis because they lead to loss of information, biased estimates, and misleading results. In practice there is a need for an imputation method to deal with missing values.

Aim: In this study a new robust regression-based imputation method to deal with missing values in longitudinal data is proposed. This method utilizes the modified adaptive linear regression model and does not require the normality of the responses. It is a novel robust imputation …

Extraction Of Fine-Grained Research Methods In The Field Of Information Science, Jiayi Hao, Yuzhuo Wang, Chengzhi Zhang

Journal of Scientific Information Research

[Purpose/significance]Research methods in information science are one of the critical research directions in this field. Constructing a fine-grained research method corpus and extracting research method entities can help scholars quickly understand the research methods in this field, explore the evolution of methods and their future development trends, and lay the foundation for the service and application of the research method corpus in the subsequent digital wave. [Method/process]Firstly, based on academic articles published in the Journal of the China Society for Scientific and Technical Information from 2000 to 2023, this study randomly selected 50 articles and manually annotated the research methodology …

Identifying Research Paths Based On Main Path Analysis: A Case Study Of Knowledge Graphs, Ruibin Wei, Yidan Wang, Yan Xu

Journal of Scientific Information Research

[Purpose/significance]The main path analysis of citation networks can be used to identify important literature in specific fields and can achieve the extraction of mainstream research threads. This paper will use the main path analysis method to analyze the research path of knowledge graphs and sort out the context of their research development. [Method/process]This paper firstly obtains research papers in the field of knowledge graphs from the Web of Science platform, then uses the HistCite software to generate a direct citation network of the literature, and then imports the data into Pajek to generate multiple main paths of the dataset, and …

Association Between Lifetime Interpersonal Violence And Post– Covid-19 Condition Among Women In Kentucky, 2020-2022, Ayşe Güler, Heather M. Bush, Katie Schill, Nurlan Kussainov, Ann L. Coker

Biostatistics Faculty Publications

Objective: The COVID-19 pandemic increased the risk of interpersonal violence. We investigated the association between lifetime interpersonal violence experience and risk of post–COVID-19 condition (the persistence of symptoms of COVID-19 and severity of health problems associated with COVID-19 that last a few weeks, months, or years) among women with lifetime interpersonal violence experience.   Methods: Women participants aged ≥18 years in Kentucky’s Wellness, Health & You—COVID-19 study completed online quantitative surveys about the impacts of the pandemic, developing COVID-19, and symptoms of post–COVID-19 condition. We conducted cross-sectional analyses estimating rate ratios of developing COVID-19 and symptoms of post–COVID-19 condition during the …

Elements Of Statistics, Paul Flesher, Jeffrey Sadler, Jonathan Rehmert, Lanee Young

All Open Educational Resources

This undergraduate text, intended for an introductory statistics course, motivates and develops basic inferential statistics. The first chapter establishes the necessity of inferential statistics, lays the basis of a scientific worldview, and finishes by introducing sampling methods and variables. Subsequent chapters develop visualizations, descriptive statistics, probability, and random variables. Sampling distributions are treated in the fifth chapter which is immediately followed by the development of confidence intervals and hypothesis testing. The text concludes with a treatment of linear regression. The use of Excel is emphasized throughout. The text is best viewed online through LibreTexts.